Grade 2 Math in Focus Chapter 1, Lessons 1-4 Kate Allen, Barnard School

In this extensively scripted collection of lessons, second graders review important concepts taught in first grade. Using scores of visuals and manipulatives, concepts are reviewed on a deeper level that simple calculation. Sentence frames are frequent, as is modeling. Students are given many opportunities for meaningful output class-wide and with a partner.

Allen Lesson 1

Big Idea: Students will be able to count and compare numbers to 1,000.

Class: Grade 2, Chapter 1 Date: Day 1

Content Objectives: • SWBAT review counting to 100 using

number bonds and ten frames. • SWBAT review counting on from a given

number & use objects to represent a number.

• SWBAT will be able to count using objects that represent numbers to 100.

Language Objectives: • SWBAT orally explain vocabulary terms • SWBAT explain thinking to a

partner/teacher orally in complete sentences.

Key Vocabulary: hundreds tens ones number bond part-part-whole ten frame add

Materials: Ten-frame models Base-ten blocks Whiteboard, markers Number cards Straws (to show groups of 10) Classwork/Homework sample

Higher Order Questions: • What is a number bond? Why do we use it? • How does a ten frame help us to count? • Why are base-ten blocks called base-ten blocks? Time: 5min

Activities: SHARED HISTORY/BUILDING BACKGROUND T: We are starting out the year in math by becoming experts on numbers. In 1st grade we learned to count in different ways. Today, in math, we will review the 4 different ways you learned to count in 1st grade. Our language objectives for today are to explain vocabulary and our thinking using complete sentences. T: Show blank number bond. What is the name for this? (point to number bond) Take student answers, write on the board. Teacher expects students to say number bond. Then, T writes the number 9 in the left side of the number bond. What 2 numbers make the number 9 when we put them together? Expected answers are 1+8 and 2+7. Show _____ (part) + ______ (part)= ___________ (whole)on whiteboard. Great! 1(part) and 8(part) = 9 (whole) AND 2(part) and 7(part )= 9(whole) We just made a number bond! Today, you will have a chance to make your own number

Allen Lesson 1

5 min 5min 5 min

bonds with your classmates. MODEL: Choose 2 volunteers. Give each volunteer 1 number. Teacher has 1 card as well. Students and teacher show class their numbers i.e. 2, 3, & 5. Q: Do we all make a number bond? Why or why not? Yes, we make a number bond because each part makes a whole when they are added together. Show 2(part)+3(part) = 5(whole) Add to word wall at the end of the lesson with picture of number bond: 2(part)+3(part) = 5(whole) HANDS ON: T: Now you will all have a chance to make your own number bonds with each other. Distribute number cards to students. Repeat directions: When I say go, you will find 2 other students to make your number bond. Remember, each group of 3 students will have a PART, PART & A WHOLE when you are finished. You can check the board to help you as you work together. Give students 3-5 minutes to work. Teacher will facilitate student work by assisting students in finding their matches. Then, bring students back to share their examples. Teacher will write examples on the whiteboard to share student work samples. Why do we use a number bond to help us count? T: We just reviewed one way we learned to count in 1st grade. We also learned of another way to count in 1st grade. Show students a blank ten frame along with: This is a __________ __________. Point to ten frame. What is this a picture of? Expected answer: ten frame If students do not remember, fill in each box of the ten frame with a circle. How many circles fit in the frame? 10. Yes! So, how does a ten frame help us to count? Expected answer: A ten frame helps us to count by making groups of 10. Refer to whiteboard. Point to number bond. What is this? Point to ten frame. What is this? Pointing to each way of counting will reinforce the differences of each way. Then, show and call on 2 students to display 2 completed ten frames. Explain to the rest of the class that when we are counting, they need to show me they are counting by showing 2 hands to represent the number 10 and 1 finger to show counting by 1. T: What number do we have now? Students should show 2 sets of hands to represent the number 20. Then, add 3 more to another blank ten frame. What number did I make now? Students should show 2 sets of hands to show 20. Then, 1 finger 3 times to show the number 23. T: We just reviewed two ways of counting. What were the 2 ways of counting we just talked about?

Allen Lesson 1

10 min 5 min

The two ways of counting we learned were _______________ and _________________. Expected answers are making number bonds and using ten frames. Great! We will review another way of counting we learned in 1st grade. Teacher will count out 10 straws having students count aloud with teacher. Stop at 10. We just made a group of 10. Put a rubber band around the group of 10 and ask for student volunteer to hold it. Let’s make another group of 10. Teacher will count out 10 more straws having students count aloud with teacher. Stop at 10. We just made another group of ten. What number did we just make? Point to each student volunteer. We count by 10. 10, 20. What number do we have now? 10+10=20. Repeat this process counting to 40 with 2 more student volunteers. The other students will show their counting with their hands. Then, count by 1’s to 43. Add this to chart on whiteboard. Have student volunteers return to the carpet. Show students base-ten blocks. What do we call these? Expected answer: The blocks are base-ten blocks. Why are these called base-ten blocks? Expected answer: They are called base-ten blocks because you need 10 before you can move to the next block. For example, you need 10 ones before you can move to one rod. You need 10 rods before you can use one hundred. Count out 10 one cubes with students just like counting with straws. Repeat twice to get to 20. Then, add 2 more rods to count to 40. Then, 3 more ones to count to 43. How did we practice counting? Expected student answer: We used straws to make groups of 10. You can also use base-ten blocks. Great! What were the other ways we learned to count? We learned to count by ______________, _________________, & _____________. Expected answers: We learned to count by using number bonds, ten frames, and by using straws to make groups of ten. Great! We will review one more way of counting. Post 100 chart on the whiteboard. This is a hundred chart. Circle the number 59. What number is this? Let’s count on aloud together as I point to each number. Count on with students and stop at the number 63. Repeat the same process starting with the number 96 and count to 100.

• What did we just do together? Expected answer: We counted on from a number.

• How did we count? Expected answer: We counted one square at a time. Great! That means we counted by 1’s.

Closure: • What did we learn today in math?

Allen Lesson 1

Time: 5min 5 min 5min 5 min

Activities: SHARED HISTORY/BUILDING BACKGROUND T: We are starting out the year in math by becoming experts on numbers. In 1st grade we learned to count in different ways. Today, in math, we will review the 4 different ways you learned to count in 1st grade. Our language objectives for today are to explain vocabulary and our thinking using complete sentences. T: Show blank number bond. What is the name for this? (point to number bond) Take student answers, write on the board. Teacher expects students to say number bond. Then, T writes the number 9 in the left side of the number bond. What 2 numbers make the number 9 when we put them together? Expected answers are 1+8 and 2+7. Show _____ (part) + ______ (part)= ___________ (whole)on whiteboard. Great! 1(part) and 8(part) = 9 (whole) AND 2(part) and 7(part )= 9(whole) We just made a number bond! Today, you will have a chance to make your own number bonds with your classmates. MODEL: Choose 2 volunteers. Give each volunteer 1 number. Teacher has 1 card as well. Students and teacher show class their numbers i.e. 2, 3, & 5. Q: Do we all make a number bond? Why or why not? Yes, we make a number bond because each part makes a whole when they are added together. Show 2(part)+3(part) = 5(whole) Add to word wall at the end of the lesson with picture of number bond: 2(part)+3(part) = 5(whole) HANDS ON: T: Now you will all have a chance to make your own number bonds with each other. Distribute number cards to students. Repeat directions: When I say go, you will find 2 other students to make your number bond. Remember, each group of 3 students will have a PART, PART & A WHOLE when you are finished. You can check the board to help you as you work together. Give students 3-5 minutes to work. Teacher will facilitate student work by assisting students in finding their matches. Then, bring students back to share their examples. Teacher will write examples on the whiteboard to share student work samples. Why do we use a number bond to help us count? T: We just reviewed one way we learned to count in 1st grade. We also learned of another way to count in 1st grade. Show students a blank ten frame along with: This is a __________ __________. Point to ten frame. What is this a picture of? Expected answer: ten frame If students do not remember, fill in each box of the ten frame with a circle. How many circles fit in the frame? 10. Yes! So, how does a ten frame help us to count? Expected answer: A ten frame helps us to count by making groups of 10. Refer to whiteboard. Point to number bond. What is this? Point to ten frame. What is this? Pointing to each way of counting will reinforce the differences of each way. Then, show and call on 2 students to display 2 completed ten frames. Explain to the rest of the class that when we are counting, they need to show me they are counting

Allen Lesson 1

Allen Lesson 1

Allen Lesson 2

Big Idea: Students will be able to count and compare numbers to 1,000.

Class: Grade 2, Chapter 1 Date: Day 2

Content Objectives: • SWBAT use base-ten blocks to represent

numbers. • SWBAT count on by ones, tens, &

hundreds.

Language Objectives: • SWBAT orally explain vocabulary terms. • SWBAT explain thinking to a

partner/teacher orally in complete sentences.

Key Vocabulary: hundreds tens ones place-value base-ten blocks represent

Materials: Magnetic base-ten blocks Whiteboard, markers Place Value Chart (teacher model) Place Value Charts (student copies) Baggies of base-ten blocks for students Homework sample

Higher Order Questions: • What is place-value? • Why do we call base-ten blocks “base-ten blocks?” Time: 7 min 2 min

Activities: SHARED HISTORY/BUILDING BACKGROUND T: Yesterday, we reviewed the ways we learned to count in 1st grade. What ways of counting did we review yesterday? Teacher will refer to chart made with students from previous lesson. Teacher will point to each way of counting discussed to assist students with their thinking.

• Turn to the 2nd grade friend sitting next to you and take turns sharing one way of counting we reviewed yesterday. Be prepared to share your thinking when we come back together as a group. Listen to and guide student discourse.

• Clap rhythm to bring students back as a group. Be prepared to share your thinking with the class. Teacher will listen to student responses to assess knowledge & retention of material from previous lesson.

Today, we will focus more on counting on by ones, tens, and hundreds using base-ten blocks. We will use base-ten blocks to represent numbers. Explain that “represent” means to show. Our language objectives for today are to explain vocabulary and our thinking using complete sentences. T: Why are base-ten blocks called “base-ten blocks?” Expected answers include: Base-ten blocks are called base-ten blocks because they help us to count in groups of ten.

Allen Lesson 2

5 min 12 min

T: Great! We will use base-ten blocks and this chart. T: Show a blank place value chart. What is the name for this? Point to and say each vocabulary term asking students to repeat after me. This is a __________ ____________ ____________. Expected answer: This is a place value chart. What is place value? Explicitly teach that place value means that where a digit sits in a number tells you its value. Scaffold concept. T: Why are base-ten blocks called “base-ten blocks?” Expected answers include: Base-ten blocks are called base-ten blocks because they help us to count in groups of ten.

• Count out 5 ones on place chart in ones column. What number do I have? Why is it in the ones column?

• Count out the number 10. What number do I have? Show students that 10 ones is also one rod. What column should it go in? Show students that 10 can go in the ones place, but it should really be moved to the tens place. Explain that the “1” is in the tens place and the “0” is in the ones place to show that we have one group of ten. T: Why are base-ten blocks called “base-ten blocks?” Expected answers include: Base-ten blocks are called base-ten blocks because they help us to count in groups of ten.

• Show the number 11. How do we show 11 on the place value chart? Students

should be able to explain that we have one group of ten and one left over. So, one rod goes in the tens place and one one goes in the ones place.

• Continue this process until we reach the number 20. • Then, use rods to count to 100 in the tens place. • What do we do when we have ten tens or ten rods? What number did we make?

Is there another way to show 100? Explain that 10 rods is the same as one flat. One flat is placed in the hundreds column and we do not have anything in the tens or ones place to represent 0.

What is place value? Expected answer: Place value means that where a number sits in a number tells you its value.

• Use 2 hundred squares, 6 ten-rods, and 3 unit cubes to represent 263. What number did I make? Expected answer: 263

• What happens if I add one more ten-rod? What number do I have now? Expected answer: 273

• What happened to the value of the number in the tens place? Expected answer: The value changed by 10 or the value changed from 6 tens to 7 tens or the value of the tens place changed from 60 to 70.

Allen Lesson 2

5 min 5 min 20 min

• Repeat process using the numbers, 352 – 362, 145-155, 231-331, & 617-717. What are we practicing? Expected answer: We are practicing using base-ten blocks to represent or show numbers. We are counting on by ones, tens, and hundreds. Teacher will point to objectives to guide student thinking.

• Now that we have practiced representing numbers together using base-ten blocks, you will have a chance to practice on your own.

MODEL: HANDS ON:

• T: Now that we have practiced representing numbers together using base-ten blocks, you will have a chance to practice on your own.

• Show students the materials they will be using. Show a bag of base-ten blocks that includes ones, tens, and hundreds. Show students their own copy of a place-value chart.

• When you go back to your seat, you will use your own base-ten blocks to represent numbers on your place value chart. I will give you a number to make using your base-ten blocks. For example, make the number 112. Model on teacher place value chart thinking aloud. The number is one hundred twelve. So, first I need one hundred. Then, I need one ten. Last, I need 2 ones. What number did I make?

• Then, I will ask you change a place value. For example, what number do we have if we add one more ten? Teacher adds one more ten to sample place value chart. Expected answer: 122

• What number do we have if we add one more hundred? Expected answer: 222 • What number do we have if we add 3 more ones? Expected answer: 225 • I need a quiet hand to share with me and the class what you will do when you

receive your tools and go back to your seat? Expected answer: We will wait for the teacher to say a number so we can represent that number with our base-ten blocks.

• The teacher then distributes materials to each student and they return to their seats with their individual supplies.

• Teacher then practices with students using numbers 260, 360, 460, 560, 660, & 760 while monitoring student progress walking around classroom to assess individual student achievement. *Underline on the board the place value that is changing. Remind students that you do not change any other place value.

• Then, teacher continues process with numbers 435, 535, 635, 735, 835, 935. • Teacher continues process with 468, 478, 488, 498, 508, 518, & 528. • With your group, take turns and make up your own number with your base-ten

blocks. Then, practice changing each place value by a number of your choice and saying what that number is. Remember, to explain to each other how the value of your number changed. The teacher will then facilitate group work by walking around classroom to assess individual student progress.

T: Stop class. What have we been practicing today during math? We are practicing _________________________________.

Allen Lesson 2

4 min

Expected answer: We are practicing how to represent numbers using base-ten blocks and counting on by ones, tens, and hundreds. T: Great! What was one thing you learned in math today? Use name cup to call on students to assess understanding of objectives. Follow-up with students not mastering concept. T: For homework tonight, you will have more time to practice counting on by ones, tens, and hundreds using base-ten blocks. *Use Math-in-Focus Extra Practice, Chapter 1, pages 1+2 for homework.

If time, show virtual base-ten block manipulatives from Math-in-Focus.

Allen Lesson 2

Allen Lesson 2

Allen Lesson 3

Big Idea: Students will be able to count and compare numbers to 1,000.

Class: Grade 2, Chapter 1 Date: Day 3

Content Objectives: • SWBAT use base-ten blocks to represent

numbers. • SWBAT write numbers in standard form,

word form, and expanded form.

Language Objectives: • SWBAT orally explain vocabulary terms • SWBAT explain thinking to a

partner/teacher orally in complete sentences.

Key Vocabulary: hundreds tens ones place-value base-ten blocks standard form word form expanded form

Materials: Magnetic base-ten blocks Whiteboard, markers Chart paper Place Value Chart (teacher model) Workbook 2A, pages 7-12 Classwork/Homework sample

Higher Order Questions: (Update) • Using your own words, explain standard form. • Using own words, explain word form. • Using your own words, explain expanded form.

Allen Lesson 3

Time: 5 min 10 min 20 min

Activities: SHARED HISTORY/BUILDING BACKGROUND T: Yesterday, we learned how to represent numbers using base-ten blocks and we learned how to count on by ones, tens, & hundreds. May I have a quiet hand volunteer to come up to the class and show how to represent the number 324 using base-ten blocks? Choose respectful volunteer. We will watch our friend show us the number 324 using base-ten blocks. What do you notice about the way our friend made the number 324? What is the value of the hundreds place? What is the value of the tens place? What is the value of the ones place? How does the value of the tens place change if I add one rod? One flat? Today, we will continue to represent numbers using base-ten blocks. We will also learn how to write numbers using standard form, word form, and expanded form. Our language objectives for today are to explain vocabulary and our thinking using complete sentences.

• Teacher will explicitly teach each vocabulary term and make a chart with the class for reference.

• For example, standard form means the showing of a number using digits or numbers. The standard form of the number 8 is 8. The standard form of 25 is 25. The standard form of 151 is 151.

• Word form means writing a number using number words. For example, the word form of 8 is eight. The word form of 25 is twenty-five. The word form of 151 is one hundred fifty-one.

• Expanded form means stretching out the number to show each place value. For example, the expanded form of 25 is 20 + 5. The expanded form of 151 is 100 + 50 + 1.

Number Standard Form Word Form Expanded Form 8 8 Eight 8 25 25 Twenty-five 20 + 5 151 151 One hundred fifty-one 100+50+1 347 347 Three hundred forty-seven 300+40+7

• Compare 3 forms to hello 3 different ways (languages) i.e. hi, hola, bonjour.

They all mean the same thing; they are just told in a different language. It is exactly the same with numbers. All 3 forms mean the same thing, but are just a different language.

• You are all going to receive a dry-erase marker to take back to your seat. We will continue to practice writing standard form, word form, and expanded form on your desks. When you get your marker, go back to your seat and show me the ready position.

Allen Lesson 3

10 min 5 min

• May I have a quiet hand share with me and the class what you will do when you get your marker? Choose a respectful, quiet hand.

• Distribute markers to students and send them back to their seats. • Write on your desks with your markers the expanded form of 45. The teacher

will walk around the room to assess student progress. Draw smiley faces on student desks for correct answers. Guide students who do not have the correct answers. When students are finished, ask for a student to come up to the board to write their response.

• Write 45 in word form. Repeat with standard form. • Teacher will monitor student progress throughout lesson. Teacher will give

students time to write and share their responses with classmates. • Say, write the expanded form of 309. • Say, write the word form of 309. • Say, write the standard form of 309. • Say, write the expanded form of 6 hundreds, 4 tens, 2 ones. Standard form? • Say, write the expanded form of 2 hundreds, 8 tens, 7 ones. Standard form?

• Take out your 2A Workbook. Open up to page 7. Review directions for pages

7-12 with students. Students will complete workbook pages independently. Teacher will monitor student progress and work with students who may be struggling with material.

Closure:

• Use name cup to share 6-8 more student responses. Collect markers and clean desks.

• For homework, students will complete Extra Practice, Math-in-Focus, Chapter 1 pages 3 & 5.

Allen Lesson 3

Allen Lesson 3

Allen Lesson 3

Allen Lesson 3

Allen Lesson 4

Big Idea: Students will be able to count and compare numbers to 1,000.

Class: Grade 2, Chapter 1 Date: Day 4

Content Objectives: • SWBAT review writing numbers correctly

in the place-value chart and writing numbers in standard, expanded, & word form.

Language Objectives: • SWBAT orally explain vocabulary terms &

concepts • SWBAT explain thinking to a

partner/teacher orally in complete sentences.

Key Vocabulary: hundreds tens ones place-value base-ten blocks standard form word form expanded form

Materials: Base-ten blocks (set of 9 unit cubes, 9 ten rods, & 9 hundred squares) “Show the Number” template Page protectors Place value chart

Higher Order Questions: (Update) • When we do we need to use word form with numbers? • When do we need to use expanded form in our daily lives? • When do we use standard form in our daily lives?

Allen Lesson 3

Time: 2 min 5 min 5 min

Activities: SHARED HISTORY/BUILDING BACKGROUND T: Yesterday, we learned how write numbers using standard form, word form, and expanded form. May I have a quiet hand volunteer to come up to the class and show the class the standard form of 45. Choose respectful volunteer. May I have a quiet hand volunteer to write the number 45 in word form? Choose respectful volunteer. May I have a quiet hand volunteer to write the number 45 in expanded form? Focus: Today, we will review writing numbers correctly in the place-value chart and writing numbers in standard, expanded, & word form. Our language objectives for today are to explain vocabulary and our thinking using complete sentences. MODEL: (Hands-on)

• Teacher will choose a volunteer to model activity for class. • Teacher will display 3 hundreds, 2 tens, & 4 ones using base-ten blocks. • How many hundred do I have? Expected response: 3 • Great! This means that I now have to write the number 3 in the hundreds. (see

sample below) • How many tens do I have? Expected answer: 2 • Fantastic! This means I now have to write 2 in the tens place. (see sample

below) • How many do I have in the ones place? Expected answer: 4 • Awesome! This means I write 4 in the ones place. (see sample below) • Now, what number did we make? How do I write this number in standard

form? Expected answer: 324 • Yes! So, I will write “324” in the row where it says standard form. Point to

row and write 324 for students. (see sample below) • When do we use standard form in our daily lives to write numbers? Expected

answers might include: We use standard form most often when we write numbers. We use standard form when we add and subtract.

• How do we write the number 324 in expanded form? Expected answer: 300+20+4

• Point to the row and write 300+20+4 for students. • When do we use expanded form in our daily lives? • Expected answer/discussion: We may not use expanded form in our daily lives

very often, but expanded form does help learn place value. • How do write the number 324 in word form? Expected answer: Three hundred

twenty-four. • Great! I will write the word form for 324 in our chart. Point to the row word

form to show students. (see sample below)

Allen Lesson 3

20 min. 10 min. 3 min.

Hundreds

Tens

Ones

3

2

4

Standard form:

324

Expanded form: 300+20+4

Word form: Three hundred twenty-four

• Now, you will have a chance to practice this with a partner! • Teacher will strategically divide class into partners and distribute materials. • Review directions with students. • Remember, player 1 shows player 2 some base-ten blocks. • Then, player 2 counts the blocks and writes the number in the place-value

chart. • Player 2 writes the number in standard form, word form, and expanded form. • Player 1 checks player 2’s answers. • Players get 1 point for every correct answer. • Take turns showing each other base-ten blocks to repeat process. • The player with the most points when time is up wins!

After about 20 minutes, bring class back together as a group for discussion and share student samples. *Each pair will present 1 number and all three forms of how to write the number to the class. Closure:

• What did we review today in math? • Teacher will use name cup to call on 6-8 students to hear student responses in

complete sentences.